Problem: $ E = \left[\begin{array}{rrr}3 & 3 & -2 \\ 4 & -2 & 2 \\ 1 & -2 & 2\end{array}\right]$ $ A = \left[\begin{array}{rr}4 & -1 \\ 0 & 3 \\ -1 & 2\end{array}\right]$ Is $ E- A$ defined?
Solution: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ E$ is of dimension $( m \times  n)$ and $ A$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ E$ ) must equal $ p$ (number of rows in $ A$ ) and 2. $ n$ (number of columns in $ E$ ) must equal $ q$ (number of columns in $ A$ Do $ E$ and $ A$ have the same number of rows? Yes Yes No Yes Do $ E$ and $ A$ have the same number of columns? No Yes No No Since $ E$ has different dimensions $(3\times3)$ from $ A$ $(3\times2)$, $ E- A$ is not defined.